Question

A tree broke from a point but did not separate. Its top touched the ground at a distance of 24 m from its base. If the point where it broke is at the height of 7 m from the ground, what is the total height of the tree?

Answer 1

Given:

• Distance between the broken top of the tree and the base of the tree = 24 m
• Point from where the tree broke is at the height of 7 m from the ground.

To find:

• Total height of the tree.

Solution:

We can find the total height of the tree using Pythagoras Theorem.

$\boxed {\mathfrak {\orange {H^{2} = P^{2}+B^{2}}}}$

Substitute the values,

H² = (7)² + (24)²

H² = 49 + 576

H² = 625

$\sf \: H = \sqrt{625}$

H = 25 m

Now, 25 m is the height of the tree that is broken.

In order to find the total height of the tre, we have to add the height of the tree that is broken and the one which is still standing there.

25 + 7 = 32 m

Total height of the tree:

Total height of the tree is 32 m.

Answer 2

The total height of the tree is 32 m.

Step-by-step explanation:

${\underline{\underline{\bf{Given:}}}}$

• The distance from the bottom point of the tree to its top point touching the ground = 24 m.
• The height of tree from the ground to the point where it is broken = 7 m.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The total height of the tree.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{Pythagorean\: Theorem:a^2+b^2=c^2}}}$

$\:\:\:\:\:\:\:\:\sf{\star\:a=Base}$

$\:\:\:\:\:\:\:\:\sf{\star\:b=Perpendicular}$

$\:\:\:\:\:\:\:\:\sf{\star\:c=Hypotenuse}$

${\underline{\underline{\bf{Solution:}}}}$

Look at the attachment! It shows the diagram of the tree. It is formed in the shape of right-angled triangle.

Here, the distance from the bottom point of the tree to its top point touching the ground is the base of the traingle. And the height of tree from the ground to the point where it is broken is the perpendicular of the triangle.

So, let's find the length of hypotenuse which is the length of broken part of the tree, by using Pythagorean Theorem:

$\leadsto{\boxed{\sf{a^2+b^2=c^2}}}$

Now, insert the measures.

$\:\:\:\:\:\:\:\::\implies{\sf{24^2+7^2=c^2}}$

$\:\:\:\:\:\:\:\::\implies{\sf{576+49=c^2}}$

$\:\:\:\:\:\:\:\::\implies{\sf{625=c^2}}$

$\:\:\:\:\:\:\:\::\implies{\sf{\sqrt{625}=c}}$

$\:\:\:\:\:\:\:\::\implies\underline{\bf{25=c}}$

Thus, the length of broken part of the tree is 25 m.

We're asked to find the total height of the tree, i.e, the sum of length of the tree from base to the broken point and the length of broken part of the tree.

$\leadsto{\sf{Perpendicular+Hypotenuse}}$

$\:\:\:\:\:\:\:\:\rightarrowtail{\sf{7+25}}$

$\:\:\:\:\:\:\:\:\rightarrowtail{\underline{\underline{\frak{\red{32\:m}}}}}$

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